Question

Mary Guilott recently graduated from Nichols State University and is anxious to begin investing her meager savings as a way of applying what she has learned in business school. Specifically, she is evaluating an investment in a portfolio comprised of two firms' common stock. She has collected the following information about the common stock of Firm A and Firm B:

	Expected Return	Standard Deviation
Firm A's Common Stock	0.15	0.18
Firm B's Common Stock	0.16	0.22
Correlation Coefficient	0.7

a. If Mary decides to invest 50% of her money in Firm A's common stock and 50% in Firm B's common stock and the correlation between the two stocks is 0.70, then the expected rate of return in the portfolio is

b. Answer part a where the correlation between the two common stock investments is equal to zero.

c. Answer part a where the correlation between the two common stock investments is equal to +1.

d. Answer part a where the correlation between the two common stock investments is equal to −1.

Answer 1

PortfolioRet = Weighted Avg Ret of securities in that portfolio.

Portfolio SD:

It is nothing but volataility of Portfolio. It is calculated based on three factors. They are
a. weights of Individual assets in portfolio
b. Volatality of individual assets in portfolio
c. Correlation betwen individual assets in portfolio.
If correlation = +1, portfolio SD is weighted avg of individual Asset's SD in portfolio. We can't reduce the SD through diversification.
If Correlation = -1, we casn reduce the SD to Sero, by investing at propoer weights.
If correlation > -1 but <1, We can reduce the SD, n=but it will not become Zero.

Wa = Weight of A
Wb = Weigh of B
SDa = SD of A
SDb = SD of B

Assume A = Firm A

B = Firm B

Part A:

Expected Ret:

Stock	Weight	Ret	WTd Ret
Firm A	0.5000	15.00%	7.50%
Firm B	0.5000	16.00%	8.00%
Portfolio Ret Return			15.50%

SD:

Particulars	Amount
Weight in A	0.5000
Weight in B	0.5000
SD of A	18.00%
SD of B	22.00%
r(A,B)	0.7

Portfolio SD = SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(A,B)]
=SQRT[((0.5*0.18)^2)+((0.5*0.22)^2)+2*(0.5*0.18)*(0.5*0.22)*0.7]
=SQRT[((0.09)^2)+((0.11)^2)+2*(0.09)*(0.11)*0.7]
=SQRT[0.0341]
= 0.1846
= I.e 18.46 %

Part B:

Expected Ret:

Stock	Weight	Ret	WTd Ret
Firm A	0.5000	15.00%	7.50%
Firm B	0.5000	16.00%	8.00%
Portfolio Ret Return			15.50%

SD:

Particulars	Amount
Weight in A	0.5000
Weight in B	0.5000
SD of A	18.00%
SD of B	22.00%
r(A,B)	0

Portfolio SD = SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(A,B)]
=SQRT[((0.5*0.18)^2)+((0.5*0.22)^2)+2*(0.5*0.18)*(0.5*0.22)*0]
=SQRT[((0.09)^2)+((0.11)^2)+2*(0.09)*(0.11)*0]
=SQRT[0.0202]
= 0.1421
= I.e 14.21 %

Part C:

Expected Ret:

Stock	Weight	Ret	WTd Ret
Firm A	0.5000	15.00%	7.50%
Firm B	0.5000	16.00%	8.00%
Portfolio Ret Return			15.50%

SD:

Particulars	Amount
Weight in A	0.5000
Weight in B	0.5000
SD of A	18.00%
SD of B	22.00%
r(A,B)	1

Portfolio SD = SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(A,B)]
=SQRT[((0.5*0.18)^2)+((0.5*0.22)^2)+2*(0.5*0.18)*(0.5*0.22)*1]
=SQRT[((0.09)^2)+((0.11)^2)+2*(0.09)*(0.11)*1]
=SQRT[0.04]
= 0.2
= I.e 20 %

PartD:

Expected Ret:

Stock	Weight	Ret	WTd Ret
Firm A	0.5000	15.00%	7.50%
Firm B	0.5000	16.00%	8.00%
Portfolio Ret Return			15.50%

SD:

Particulars	Amount
Weight in A	0.5000
Weight in B	0.5000
SD of A	18.00%
SD of B	22.00%
r(A,B)	-1

Portfolio SD = SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(A,B)]
=SQRT[((0.5*0.18)^2)+((0.5*0.22)^2)+2*(0.5*0.18)*(0.5*0.22)*-1]
=SQRT[((0.09)^2)+((0.11)^2)+2*(0.09)*(0.11)*-1]
=SQRT[0.0004]
= 0.02
= I.e 2 %